sae_metrics.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading checkpoint shards: 100%|██████████| 3/3 [00:11<00:00,  3.73s/it]\n"
     ]
    }
   ],
   "source": [
    "# download model\n",
    "from transformers import AutoModelForSequenceClassification, AutoTokenizer\n",
    "import torch\n",
    "\n",
    "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
    "model_name = \"reciprocate/dahoas-gptj-rm-static\"\n",
    "model = AutoModelForSequenceClassification.from_pretrained(model_name).to(device)\n",
    "tokenizer = AutoTokenizer.from_pretrained(model_name)\n",
    "# download SAEs\n",
    "from huggingface_hub import hf_hub_download\n",
    "from dictionary import GatedAutoEncoder\n",
    "\n",
    "# import sys\n",
    "# sys.path.append(\"/root/dictionary_learning/\")\n",
    "\n",
    "layers = [2,8,12,14,16,20]\n",
    "activation_names = [f\"transformer.h.{layer}\" for layer in layers]\n",
    "model_id = \"Elriggs/rm\"\n",
    "saes = []\n",
    "for layer in layers:\n",
    "    sae_filename = f\"ae_layer{layer}.pt\"\n",
    "    ae_download_location = hf_hub_download(repo_id=model_id, filename=sae_filename)\n",
    "    saes.append(GatedAutoEncoder.from_pretrained(ae_download_location).to(device))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloading stas/openwebtext-10k\n"
     ]
    }
   ],
   "source": [
    "# download dataset\n",
    "from datasets import load_dataset\n",
    "def download_dataset(dataset_name, tokenizer, max_length=256, num_datapoints=None):\n",
    "    if(num_datapoints):\n",
    "        split_text = f\"train[:{num_datapoints}]\"\n",
    "    else:\n",
    "        split_text = \"train\"\n",
    "    dataset = load_dataset(dataset_name, split=split_text).map(\n",
    "        lambda x: tokenizer(x['text']),\n",
    "        batched=True,\n",
    "    ).filter(\n",
    "        lambda x: len(x['input_ids']) > max_length\n",
    "    ).map(\n",
    "        lambda x: {'input_ids': x['input_ids'][:max_length]}\n",
    "    )\n",
    "    return dataset\n",
    "\n",
    "dataset_name = \"stas/openwebtext-10k\"\n",
    "max_seq_length = 40\n",
    "print(f\"Downloading {dataset_name}\")\n",
    "dataset = download_dataset(dataset_name, tokenizer=tokenizer, max_length=max_seq_length, num_datapoints=7000) # num_datapoints grabs all of them if None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/219 [00:00<?, ?it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 219/219 [04:13<00:00,  1.16s/it]\n"
     ]
    }
   ],
   "source": [
    "# Save metrics\n",
    "import torch\n",
    "from torch.utils.data import DataLoader\n",
    "from einops import rearrange\n",
    "from tqdm import tqdm\n",
    "from baukit import TraceDict\n",
    "batch_size = 32\n",
    "l0s = [[] for _ in layers]\n",
    "cos_sims = [[] for _ in layers]\n",
    "fvus = [[] for _ in layers]\n",
    "l2_ratios = [[] for _ in layers]\n",
    "variances = [[] for _ in layers]\n",
    "with torch.no_grad(), dataset.formatted_as(\"pt\"):\n",
    "    dl = DataLoader(dataset[\"input_ids\"], batch_size=batch_size)\n",
    "    for i, batch in enumerate(tqdm(dl)):\n",
    "        batch = batch.to(model.device)\n",
    "        with TraceDict(model, activation_names) as ret:\n",
    "            _ = model(batch).logits\n",
    "        for layer_ind, layer in enumerate(layers):\n",
    "            internal_activations = ret[activation_names[layer_ind]].output\n",
    "            # check if instance tuple\n",
    "            if(isinstance(internal_activations, tuple)):\n",
    "                internal_activations = internal_activations[0]\n",
    "            \n",
    "            sae = saes[layer_ind]    \n",
    "            x = rearrange(internal_activations, \"b s n -> (b s) n\" )\n",
    "            features = sae.encode(x)\n",
    "            x_hat = sae.decode(features)\n",
    "            l0 = (features != 0).sum(-1).float().mean().item()\n",
    "            cos_sim = torch.nn.functional.cosine_similarity(x, x_hat, dim=-1).mean().item()\n",
    "            fvu = ((x - x_hat) ** 2).mean() / x.var()\n",
    "            var = x.var().item()\n",
    "            l2_ratio = (torch.norm(x, p=2, dim=-1) / torch.norm(x_hat, p=2, dim=-1)).mean().item()\n",
    "            l0s[layer_ind].append(l0)\n",
    "            cos_sims[layer_ind].append(cos_sim)\n",
    "            fvus[layer_ind].append(fvu.item())\n",
    "            l2_ratios[layer_ind].append(l2_ratio)     \n",
    "            variances[layer_ind].append(var)\n",
    "# batch_size = 128\n",
    "# dictionary_activations, tokens_for_each_datapoint = get_dictionary_activations(model, dataset, activation_name, max_seq_length, ae, batch_size=batch_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot l0 vs cos_sim for each, overlapping in a scatter plot\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "for layer_ind, layer in enumerate(layers):\n",
    "    \n",
    "    # plt.scatter(l0s[layer_ind], cos_sims[layer_ind], label=f\"Layer {layer}\")\n",
    "    # above but mean of each\n",
    "    l0 = sum(l0s[layer_ind])/len(l0s[layer_ind])\n",
    "    cos_sim = sum(cos_sims[layer_ind])/len(cos_sims[layer_ind])\n",
    "    plt.scatter(l0, cos_sim, label=f\"Layer {layer}\")\n",
    "plt.xlabel(\"L0\")\n",
    "plt.ylabel(\"Cosine Similarity\")\n",
    "plt.legend()\n",
    "plt.title(\"L0 vs Cosine Similarity\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Layer 2 L0: 131\n",
      "Layer 8 L0: 53\n",
      "Layer 12 L0: 56\n",
      "Layer 14 L0: 44\n",
      "Layer 16 L0: 22\n",
      "Layer 20 L0: 13\n"
     ]
    }
   ],
   "source": [
    "for layer_ind, layer in enumerate(layers):\n",
    "    \n",
    "    # plt.scatter(l0s[layer_ind], cos_sims[layer_ind], label=f\"Layer {layer}\")\n",
    "    # above but mean of each\n",
    "    l0 = sum(l0s[layer_ind])/len(l0s[layer_ind])\n",
    "    print(f\"Layer {layer} L0: {l0:.0f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# also plot l0 vs fvu\n",
    "for layer_ind, layer in enumerate(layers):\n",
    "    l0 = sum(l0s[layer_ind])/len(l0s[layer_ind])\n",
    "    fvu = sum(fvus[layer_ind])/len(fvus[layer_ind])\n",
    "    plt.scatter(l0, fvu, label=f\"Layer {layer}\")\n",
    "plt.xlabel(\"L0\")\n",
    "plt.ylabel(\"FVU\")\n",
    "plt.legend()\n",
    "plt.title(\"L0 vs FVU\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# also plot l0 vs l2_ratio\n",
    "for layer_ind, layer in enumerate(layers):\n",
    "    l0 = sum(l0s[layer_ind])/len(l0s[layer_ind])\n",
    "    l2_ratio = sum(l2_ratios[layer_ind])/len(l2_ratios[layer_ind])\n",
    "    plt.scatter(l0, l2_ratio, label=f\"Layer {layer}\")\n",
    "plt.xlabel(\"L0\")\n",
    "plt.ylabel(\"L2 Ratio\")\n",
    "plt.legend()\n",
    "plt.title(\"L0 vs L2 Ratio\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'FVU vs Cosine Similarity')"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# now FVU vs cos sim. Color by L0\n",
    "for layer_ind, layer in enumerate(layers):\n",
    "    # l0 = sum(l0s[layer_ind])/len(l0s[layer_ind])\n",
    "    fvu = sum(fvus[layer_ind])/len(fvus[layer_ind])\n",
    "    cos_sim = sum(cos_sims[layer_ind])/len(cos_sims[layer_ind])\n",
    "    plt.scatter(fvu, cos_sim,  label=f\"Layer {layer}\")\n",
    "plt.xlabel(\"FVU\")\n",
    "plt.ylabel(\"Cosine Similarity\")\n",
    "# plt.colorbar()\n",
    "plt.legend()\n",
    "plt.title(\"FVU vs Cosine Similarity\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f7d1c4bb460>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot var by fvu\n",
    "for layer_ind, layer in enumerate(layers):\n",
    "    fvu = sum(fvus[layer_ind])/len(fvus[layer_ind])\n",
    "    var = sum(variances[layer_ind])/len(variances[layer_ind])\n",
    "    plt.scatter(fvu, var, label=f\"Layer {layer}\")\n",
    "plt.xlabel(\"FVU\")\n",
    "plt.ylabel(\"Variance\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(0.0019, device='cuda:0')"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape, features.shape, x_hat.shape\n",
    "cos_sim = torch.nn.functional.cosine_similarity(x_hat, x, dim=-1).mean().item()\n",
    "features.shape\n",
    "(features != 0).sum(-1).float().mean().item(), (features != 0).sum(-1).float()\n",
    "# norm of x_hat/ x\n",
    "l2_ratio = (torch.norm(x_hat, dim=-1)/ torch.norm(x, dim=-1)).mean().item()\n",
    "l2_ratio\n",
    "fvu = ((x - x_hat)**2).mean() / (x**2).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([1280, 4096]), torch.Size([1280]), torch.Size([1280, 32768]))"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_hat.shape, torch.norm(x_hat, dim=-1).shape, features.shape"
   ]
  }
 ],
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